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Alex73 [517]
3 years ago
10

Solve: 2x+7/5 - x-3/10 = x+1/15find the value of x and verify the result will RHS ​

Mathematics
2 answers:
liraira [26]3 years ago
8 0

Answer:

Step-by-step explanation:

100+5

105

choli [55]3 years ago
5 0

Step-by-step explanation:

<h3><u>Given Question :- </u></h3>

Solve for x :-

\dfrac{2x + 7}{5} -  \dfrac{x - 3}{10}  =  \dfrac{x + 1}{15}

\red{\large\underline{\sf{Solution-}}}

Given linear equation is

\rm :\longmapsto\: \dfrac{2x + 7}{5} -  \dfrac{x - 3}{10}  =  \dfrac{x + 1}{15}

\rm :\longmapsto\: \dfrac{2(2x + 7) - (x - 3)}{10}  =  \dfrac{x + 1}{15}

\rm :\longmapsto\: \dfrac{4x + 14 - x  +  3}{10}  =  \dfrac{x + 1}{15}

\rm :\longmapsto\: \dfrac{(4x - x)  + (14 + 3)}{10}  =  \dfrac{x + 1}{15}

\rm :\longmapsto\: \dfrac{3x  + 17}{10}  =  \dfrac{x + 1}{15}

On multiply by 5 on both sides,

\rm :\longmapsto\: \dfrac{3x  + 17}{2}  =  \dfrac{x + 1}{3}

On cross multiplication, we get

\rm :\longmapsto\:3(3x + 17) = 2(x + 1)

\rm :\longmapsto\:9x +51 = 2x + 2

\rm :\longmapsto\:9x  - 2x = 2 - 51

\rm :\longmapsto\:7x = - 49

\bf\implies \:x =  - 7

<h3><u>VERIFICATION</u></h3>

Consider, LHS

\red{\rm :\longmapsto\: \dfrac{2x + 7}{5} -  \dfrac{x - 3}{10}}

On substituting the value of x, we get

\red{\rm \:  =  \:  \dfrac{2( - 7) + 7}{5} -  \dfrac{ - 7 - 3}{10}}

\red{\rm \:  =  \:  \dfrac{ - 14 + 7}{5} -  \dfrac{ - 10}{10}}

\red{\rm \:  =  \:  \dfrac{ - 7}{5}  + 1}

\red{\rm \:  =  \:  \dfrac{ - 7 + 5}{5}}

\red{\rm \:  =  \:  \dfrac{ - 2}{5}}

Consider RHS

\green{\rm :\longmapsto\:\dfrac{x + 1}{15}}

On substituting the value of x, we get

\green{\rm \:  =  \: \dfrac{ - 7 + 1}{15}}

\green{\rm \:  =  \: \dfrac{ - 6}{15}}

\green{\rm \:  =  \: \dfrac{ - 2}{5}}

\rm \implies\:LHS=RHS

HENCE, VERIFIED

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